Although synchronization effects play an important role in many areas of basic and applied science, their treatment in undergraduate physics courses requires more attention. Based on acoustic experiments with a driven organ pipe, the article proposes analytical, numerical and qualitative approaches to this universal phenomenon, suitable for introductory teaching. The Adler equation is developed, a first-order nonlinear differential equation describing the phase dynamics of driven self-sustained oscillations in the weak coupling limit. Analytical solutions, intuitive mechanical analogues and properties of the resulting comb spectra are discussed. The underlying phase model is paradigmatic for synchronization-based self-organization phenomena in a wide range of fields, from physics and engineering to life and social sciences.

中文翻译：

---

通用同步：声学实验、相位振荡器模型和机械模拟

尽管同步效应在基础科学和应用科学的许多领域发挥着重要作用，但它们在本科物理课程中的处理需要更多的关注。基于驱动风琴管的声学实验，本文提出了针对这一普遍现象的分析、数值和定性方法，适合入门教学。建立了阿德勒方程，这是一个一阶非线性微分方程，描述弱耦合极限下驱动自持振荡的相位动力学。讨论了分析解决方案、直观的机械模拟以及所得梳状光谱的特性。底层相位模型是从物理和工程到生命和社会科学等广泛领域中基于同步的自组织现象的范例。